# Suppose you are given the following information

Suppose you are given the following information. The beta of company i, b(i), is 1.1, the risk free rate, r(rf), is 7 percent, and the expected market premium, r(m) - r(rf), is 6.5 percent. (Assume that a(i) = 0.0)

a. Use the Security Market Line (SML) or CAPM to find the required return for this company.

b. Because your company is smaller than average and more successful than average (that is, it has a low book-to-market ratio), you think the Fama-French three factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-Franch three-factor model: The coefficient for the size effect, c(i), is 0.7, and the coefficient for the book-to-market effect is d(i) is -0.3. If the expected value of the size factor is 5 percent and the expected value of the book-to-market factor is 4 percent, what is the required return using the Fama-French three-factor model?

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a. Use the Security Market Line (SML) or CAPM to find the required return for this company.

Capital Asset Pricing Model (CAPM) is equation in modern portfolio theory expressing the idea that securities in the market are priced so that their expected return will compensate investors for their expected risk.

The risk factor beta is calculated in terms of the chosen asset class.

CAPM is used theoretically, to relate securities to the market as a whole, and practically, as the discount rate in discounted cash flow calculations to establish the fair value of an investment.

Applying the CAPM formula:

Rr = Rf + Beta*(Rm-Rf) = 7%+1.1*6.5% = 14.2%

So the required return for this company is ...

Unique Linear Polynomial that Contains Two Points

a. Consider the simplest case of a linear polynomial f(x) = mx + b.

Suppose f(?) = 0 and f(0) = ?. Does this information allow you to find m and b? Explain.

b. Now we look at a quadratic function

f(x)=ax^2 +bx+c.

Suppose ?1 does not equal ?2 and f(?1) = f(?2) = 0. How much does this information allow you to conclude about f(x)? Explain. If you are given the value f(0) does this always allow you to find f(x)? Explain.

*c.* Suppose f(x) is a polynomial of degree d>0. Suppose x_1,...,x_d+1 and y_1,...,y_d+1 are real numbers, with the x_s distinct from one another, and you are given that

f(x_i)=y_i, for i=1,2,...,d+1.

Explain why the polynomial f is uniquely determined (that is there is one and only one such polynomial f(x)) and write down an expression for f.